I'm standing at a safe distance from a black hole and I'm in an Earthlike time frame of reference. Through my telescope I see a man starts to fall towards the black hole. I have looked at this question but it doesn't quite get to what I'm looking for.
I watch him accelerate towards the black hole until I know that he is getting close to $c$. But, the gravitational time dilation surrounding the black hole would be so great that I would actually see him slow down rather than speed up? And then just a short distance above the event horizon, gravitational time dilation would be so great that I would see him nearly stop, so that even the 14 billion year ago of the universe would not be long enough for him to actually reach the event horizon. Help me to understand this? How can he be falling at near $c$ at the same time that he is nearly stopped?
Of course, in his own frame, he just sees himself falling towards the black hole and never reaching it in the short time involved. He would be facing both kinetic and gravitational time dilation.
Help me to envision this from my frame.